Vectors and Vector Addition

Examples of solutions

Problem 1

Hearing rattles from a snake you make two rapid displacements of magnitude 8.0 and 6.0 m. Show how your displacements might add to give a resultant of magnitude
a) 14.0 m;
b) 2.0 m;
c) 10.0 m.

Problem 2

A postal employee drives a delivery truck along a route which is 2.6 km North followed by 4.0 km East, and 3.1 at 45°km North of East. Find the magnitude and direction of the resultant displacement.

Problem 3

For the vectors A and B find the magnitude and direction of
a) the vector sum A + B;
b) the vector difference A - B ;
c) -A - B;
d) B - A.

Problem 4

A spelunker is surveying a cave. He follows a passage that goes 210 m straight west, then 180 m in a direction 45° east of north, then 110 m at 60° east of south. After a fourth unmeasured displacement he finds himself back at the start. Determine the magnitude and direction of the fourth displacement.

Problem 5

Find the x and y components of the following vectors. In each case the magnitude of the vector and the angle, measured counterclockwise, that it makes with the +x-axis are given,
a) magnitude 7.40 m, angle 30°;
b) magnitude 15 km, angle 225°;
c) magnitude 9.30 cm, angle 323°.

Problems for solution without assistance

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